An analysis of electrical conductivity model in saturated porous media

Electrical conductivity of saturated porous media has numerous applications in many fields. In recent years, the number of theoretical methods to model electrical conductivity of complex porous media has dramatically increased. Nevertheless, the process of modeling the spatial conductivity distributed function continues to present challenges when these models used in reservoirs, particularly in porous media with strongly heterogeneous pore-space distributions. Many experiments show a more complex distribution of electrical conductivity data than the predictions derived from the experiential model. Studies have observed anomalously-high electrical conductivity of some low-porosity (tight) formations compared to more- porous reservoir rocks, which indicates current flow in porous media is complex and difficult to predict. Moreover, the change of electrical conductivity depends not only on the pore volume fraction but also on several geometric properties of the more extensive pore network, including pore interconnection and tortuosity. In our understanding of electrical conductivity models in porous media, we study the applicability of several well-known methods/theories to electrical characteristics of porous rocks as a function of pore volume, tortuosity and interconnection, to estimate electrical conductivity based on the micro-geometrical properties of rocks. We analyze the state of the art of scientific knowledge and practice for modeling porous structural systems, with the purpose of identifying current limitations and defining a blueprint for future modeling advances. We compare conceptual descriptions of electrical current flow processes in pore space considering several distinct modeling approaches. Approaches to obtaining more reasonable electrical conductivity models are discussed. Experiments suggest more complex relationships between electrical conductivity and porosity than experiential models, particularly in low-porosity formations. However, the available theoretical models combined with simulations do provide insight to how microscale physics affects macroscale electrical conductivity in porous media.